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37"? 


The  Temperature    Coefficient   of   the 

Weight  of  a  Falling  Drop  as  a  Means 

of  Estimating  the  Molecular 

Weight  and  the  Critical 

Temperature  of  a 

Liquid* 


DISSERTATION 

SUBMITTED   IN  PARTIAL  FULFILLMENT  OF  THE  REQUIRE- 
MENTS FOR  THE  DEGREE  OF  DOCTOR  OF  PHILOSOPHY 
IN  THE  FACULTY   OF  PURE  SCIENCE  IN  COLUMBIA 
UNIVERSITY  IN  THE  CITY  OF  NEW  YORK. 


BY 

ERIC  HIGGINS 

NEW  YORK  CITY 

1908 


EASTON,  PA.  : 
ESCHRNBACH  PRINTING  COMPANY. 

I90S. 


The  Temperature    Coefficient   of  the 

Weight  of  a  Falling  Drop  as  a  Means 

of  Estimating  the  Molecular 

Weight  and  the  Critical 

Temperature  of  a 

Liquid* 


DISSERTATION 

SUBMITTED  IN  PARTIAL  FULFILLMENT  OF  THE  REQUIRE- 
MENTS FOR  THE  DEGREE  OF  DOCTOR  OF  PHILOSOPHY 
IN  THE  FACULTY  OF  PURE  SCIENCE  IN  COLUMBIA 
UNIVERSITY  IN  THE  CITY  OF  NEW  YORK. 


BY 


ERIC  HIGGINS 

NEW  YORK  CITY 

1908 


EASTON,  PA.  : 

ESCHBNBACH  PRINTING  COMPANY. 
1908. 

^^ 

OF  THE 


UNIVERSITY 


OF 


CONTENTS. 

Page. 

Introduction  and  Object  of  Investigation 5 

Apparatus  and  Method 6 

Results 10 

Discussion  of  Results 16 

Summary 18 

PART  II. 

On  Some  New  Formulae  Relating  Various  Constants  of  Non-asso- 
ciated Liquids 21 


183470 


ACKNOWLEDGMENT 

This  work  was  carried  out  under  the  direction  of  Professor 
J.  Livingston  Rutgers  Morgan  at  his  suggestion.  The  author 
begs  to  tender  his  sincere  thanks  for  the  assistance,  advice 
and  encouragement  accorded  to  him  during  the  course  of  the 
work  by  Professor  Morgan.  E.  H. 


' 

rHE 

UNIVERSITY  I 


The  Temperature  Coefficient   of  the 
Weight  of  a  Falling  Drop  as  a 
Means  of  Estimating  the 
Molecular  Weight  and 
the  Critical  Tem- 
perature of  a 
Liquid. 


OBJECT  OF  THE  INVESTIGATION. 

In  a  recent  paper,1  it  was  shown  that  the  weight  of  a  drop 
of  liquid  falling  from  a  properly  constructed  tip  is  proportional 
for  any  one  diameter  of  tip,  to  the  surface  tension  of  the 
liquid;  and,  further,  that  when  falling  drop  weights  are 
substituted  for  surface  tensions  as  measured  by  capillary 
rise  in  the  formula  of  Eotvos,  as  modified  and  presented 
in  two  forms  by  Ramsay  and  Shields,  the  molecular  weights 
and  critical  temperatures  of  liquids  can  be  calculated  with 
an  accuracy  equal  to  that  attained  by  the  use  of  the  surface 
tensions  found  from  the  capillary  rise. 

The  object  of  the  present  work  was  to  measure  the  magni- 
tude of  falling  drop  weights  with  the  utmost  possible  accuracy 
and  thus  to  test  the  conclusions  of  Morgan  and  Stevenson; 
to  determine  if  irregularities  in  the  constant  value  (^temp) 
were  real  or  due  to  experimental  error  and  to  conclusively 
establish  the  relative  value  of  this  method  of  determination 
of  the  molecular  weight  and  critical  temperature  as  compared 
with  other  methods  for  arriving  at  these  values.  The  results 
of  my  work,  it  may  be  said  here,  have  not  only  confirmed 
the  conclusions  of  Morgan  and  Stevenson  in  every  respect, 
as  far  as  concerns  any  one  tip,  but  in  addition  have  shown 

1  Morgan  and  Stevenson,  J.  A.  C.  S.,  30*  360-376,  1908. 


that  for  the  determination  of  relative  surface  tensions,  the 
drop  method  is  more  accurate  than  the  one  in  common  use, 
which  depends  upon  capillary  rise.  Further,  they  show 
that  the  molecular  temperature  coefficient  of  drop  weight 
K(temp)  is  really  a  constant,  although  Ramsay  and  Shields, 
for  the  same  liquids,  found  the  corresponding  molecular 
temperature  coefficient  of  surface  tension  (fe),  from  capillary 
rise,  to  vary  so  much  that  for  the  calculation  of  critical 
temperatures  it  was  necessary  to  first  find  the  exact  value 
of  k  for  the  liquid  in  question.  This  is  not  necessary  when 
working  with  drop  weights,  the  one  constant  value,  holding 
for  all  the  non-associated  liquids  studied,  and  so  presumably 
for  all  the  others.2  This  apparently  also  makes  the  drop- 
weight  method  at  its  best,  more  accurate  as  a  means  of 
determining  the  molecular  weight  than  any  other  method, 
with  the  exception  of  that  for  permanent  gases,  which  is 
based  upon  the  density. 

APPARATUS  AND  METHOD. 

The  apparatus  for  the  measurement  of  the  volume  of  a 
single  falling  drop  (Figure  i)  in  construction  was  essentially 
the  same  as  that  employed  by  Morgan  and  Stevenson,  differ- 
ing only  in  having  a  more  accurate  capillary  burette  (i  mm. 
corresponding  to  0.000,046  cc.)  and  in  having  the  tip  joined 
directly  to  it,  without  the  interposition  of  a  wider  tube. 
My  burette  was  also  of  greater  length  (2.5  meters)  thus 
allowing  drops  of  the  liquids  having  the  highest  drop  volumes 
to  be  measured  without  the  use  of  the  bulbs,  which  were 
found  to  be  a  danger  when  using  the  more  viscous  liquids, 
owing  to  drainage  difficulties.  The  smaller  diameter  of  the 
burette  enabled  me  to  obtain  more  accurate  readings,  the 
uniformity  of  the  tube  removed  difficulties  as  to  drainage, 
and  the  absence  of  a  constricted  "zero  mark"  permitted  a 
more  deliberate  and  accurate  reading.  To  obviate  the 
possible  loss  of  a  reading  due  to  the  meniscus  falling  in  a 
bend  of  the  burette  tube  or  at  the  place  where  the  joining 

2  See  second  part. 


: 

—  --_•  --,  - 

—  ...  ..._ 

1  •  •-  -  — 

."  •,-."'---'.  : 

?N    ff~ 

^ 

j 

j   'L 

|| 





| 

-. 

— 



d 



- 

_,  

- 

— 

~ 

i 



.  . 

;| 



-  1- 

:E 

0 


FIG.  i. 


THE 
UNlVPPCf-rx, 


To  HOUM    M*IH» 

ilOV 


FIG.  2. 


of  the  two  lengths  of  capillary  tubing  composing  it  had 
distorted  the  bore,  four  "zero  marks'*  at  successive  dis- 
tances of  one  centimeter  from  one  another  were  scratched 
upon  the  burette  tubing  just  above  the  tip  and  the  exact 
relative  volumes  of  the  intervals  between  them  determined. 
In  all  other  respects  the  apparatus  was  exactly  the  same  as 
that  employed  by  Morgan  and  Stevenson  and  was  operated 
in  the  same  way. 

The  dimensions  of  the  apparatus,  69  X  18  centimeters, 
introduced  difficulties  in  maintaining  a  constant  and  uni- 
form temperature.  The  electrically  heated  thermostat 
finally  adopted  for  the  purpose  is  shown  in  Figure  2,  and  the 
electrical  connections  diagrammatically  in  Figure  3.  The 
heating  coil  and  thermo-regulator  placed  in  the  outer  vessel 
(a  60  X  30  centimeter  glass  anatomical  jar)  maintained  the 
inner  cylinder  (another  jar,  60  X  20  centimeters)  in  a  bath, 
the  temperature  of  which  varied  rapidly  within  narrow 
limits.  The  variation  of  temperature  in  the  inner  vessel  was 
naturally  much  smaller  than  this,  and  it  was  found  easily 
possible  to  retain  it  constant  at  any  temperature,  from  24° 
to  76°  within  0.02°  for  any  desired  length  of  time.  I  be- 
lieve that  this  "jacket"  system  yields  the  most  satisfactory 
results  where  the  conditions  limit  the  disposition  of  the 
heating  arrangements,  and  large  instruments  are  to  be  dealt 
with.  The  vibration  of  mechanical  stirrers  being  fatal  to  the 
accurate  determination  of  drop  volumes,  the  water  in  both  the 
inner  and  outer  cylinders  was  thoroughly  agitated  by  a 
current  of  air  passing  through  block-tin  pipes.  The  trouble 
which  might  be  caused  by  the  breaking  down  of  the  syphon 
constant  level,  owing  to  the  liberation  of  dissolved  air  from 
the  cold  feed  water,  was  obviated  by  the  air  trap  shown  in 
the  figure. 

The  heating  current  being  heavy  (10  to  20  amperes  at 
no  volts)  was  found  to  be  best  broken  from  a  surface  of 
mercury  beneath  water  continually  supplied  from  the  over- 
flow of  the  constant  level.  The  current  breaker  was  operated 
by  twelve  "gravity"  cells  thrown  in  through  a  small  relay 


8 

operated  through  the  toluol  thermo-regulator  by  two  of  the 
same  cells.  By  thus  breaking  a  very  weak  current  in  the 
regulator  no  trouble  was  experienced  from  the  contamina- 
tion of  its  mercury  surface.  The  apparatus  in  this  form 
ran  continuously  at  various  temperatures  and  without 
attention  or  cleaning  for  six  months  and  gave  perfectly 
satisfactory  results,  the  only  trouble  lying  in  the  impossibility 
of  obtaining  glass  vessels  of  this  size  which  were  sufficiently 
well  annealed  to  support  the  higher  temperatures  for  more 
than  six  or  eight  weeks,  as  is  evidenced  by  the  fact  that  I 
was  forced  to  replace  these  three  times  during  the  course  of 
the  work. 

The  capillary  burette  was  calibrated  with  mercury  at  20°, 
successive  quantities  being  blown  out  and  weighed,  the 
operation  being  repeated  four  times.  The  summated  volumes 
calculated  from  these  weights  differed  from  that  calculated 
from  the  weight  of  the  total  content  (0.1230  cubic  centimeter) 
by  only  0.000,003  cubic  centimeter.  This  calibration  was 
further  checked  by  measuring  the  length  of  various  threads 
of  mercury  in  all  parts  of  the  tube,  thus  measuring  each 
centimeter  of  the  burette.  These  results  were  plotted  on  a 
curve  from  which  volumes  could  be  read  to  0.000,005  cubic 
centimeter.  In  the  calibration  in  air  the  position  of  the 
meniscus  was  read  through  an  uncorrected  lens,  taking 
advantage  of  its  lack  of  rectilinearity  to  avoid  parallax. 
In  the  estimations  in  the  thermostat  the  same  object  was 
attained  when  taking  an  observation  of  the  "zero  marks" 
by  the  use  of  narrow  slits  in  a  mask  attached  to  the  outer 
cylinder  centering  on  similar  slits  on  the  opposite  side,  from 
which  the  necessary  illumination  was  obtained  from  a  small 
electric  lamp.  The  measuring  tube  itself,  when  in  the 
thermostat,  acted  like  an  uncorrected  lens  in  making  read- 
ings of  the  values  on  the  graduated  scale. 

This  calibration  being  performed  at  20°,  it  was  necessary 
to  determine  the  effect  of  temperature  in  dilating  the  tube 
and  expanding  the  scale.  The  volume  of  a  thread  of  mercury, 
as  given  by  the  curve,  was  observed  at  every  10°,  between 


DIAGRAM  OF  ELECTRIC 
CONNECTIONS 


FIG.  3. 


5°  and  85°,  the  mercury  being  subsequently  weighed  and 
its  true  volume  calculated  at  each  of  the  temperatures. 
This  work  showed  the  effect  of  dilation  to  be  very  small, 
amounting  to  but  0.000,000,14  cubic  centimeter  per  centi- 
meter of  length  per  degree.  All  volumes  read  were  corrected 
in  accord  with  this.  The  possibility  of  a  residual  dilation 
effect  on  the  capillary  tube  after  heating  to  high  tempera- 
tures was  guarded  against  by  working  alternately  on  an 
ascending  and  descending  thermometer.  A  series  of  estima- 
tions at  one  temperature  occupying  at  least  a  day,  the  passage 
from  low  to  high,  and  again  to  low  temperature  extended 
over  periods  of  from  six  to  ten  days,  thus  reducing  to  a 
minimum  the  effect  of  residual  dilation. 

As  a  further  check  on  the  accuracy  of  our  original  calibra- 
tion and  of  our  assumption  of  the  absence  of  residual  dila- 
tion, the  total  content  of  the  burette  was  measured  three 
times  during  the  course  of  the  work  and  no  appreciable 
difference  observed. 

As  mentioned  by  Morgan  and  Stevenson,  all  difficulties 
occasioned  by  condensation  on,  or  evaporation  from,  the 
drop  when  forming  is  prevented  by  the  production  of  a 
"fog"  upon  the  walls  of  the  dropping  cup.  This  condition 
I  find  to  be  most  readily  induced  by  dusting  fine  graphite 
powder  upon  the  walls  of  the  cup  above  the  liquid.  By 
then  heating  the  liquid  to  a  temperature  of  100°  (or  as  near 
that  as  possible  without  causing  it  to  boil)  for  five  minutes 
and  plunging  the  cup  in  cold  water,  vapor  is  deposited  upon 
the  various  particles,  producing  a  satisfactory  and  durable 
fog.  The  instrument  is  then  placed  in  the  thermostat  and  a 
drop  allowed  to  hang  from  the  tip  for  an  hour.  At  the  end 
of  this  time  the  conditions  are  such  that  a  drop  neither 
gains  nor  loses  in  volume.  Before  each  measurement  I 
assured  myself,  by  drawing  the  drop  back  into  the  burette 
several  times,  that  such  a  condition  prevailed,  and  that  the 
drop  neither  gained  nor  lost  in  volume.  When  passing 
from  one  temperature  to  another  the  fog  can  be  maintained 
by  allowing  a  drop  to  hang  from  the  tip  during  the  change. 


10 

Since  a  thermometer  could  not  very  well  be  placed  in  the 
dropping  cup  itself  a  similar  cup  containing  a  fog  was  placed 
beside  the  burette,  a  certified  thermometer  taking  the  place 
of  the  tip  and  no  estimation  was  made  until  the  thermometer 
within  the  "blank"  had  agreed  with  a  similar  thermometer 
within  the  thermostat  for  a  half  hour.  Without  this  some- 
what elaborate  procedure  it  was  impossible  to  get  agreeing 
results,  drop  weight  being  very  sensitive  to  changes  in  tem- 
perature. 

To  prove  that  drainage  difficulties  were  absent,  a  short 
thread  of  liquid  was  drawn  through  the  tube  at  various 
speeds,  from  one  centimeter  to  one  millimeter  per  second, 
and  the  length  of  the  thread  measured  after  each  passage, 
but  so  long  as  the  walls  of  the  capillary  were  wetted  no 
alteration  in  volume  could  be  detected  with  any  of  the  six 
liquids  used. 

Morgan  and  Stevenson  measured  the  volume  of  a  single 
drop,  for  it  seemed  from  the  work  of  other  investigators 
that  the  successive  formation  of  several  drops  might  introduce 
complications.  My  work  has  shown  that,  in  the  presence 
of  a  perfect  fog  and  constant  temperature,  a  succession  of 
drops  (i.  e.,  where  the  clinging  drop  remaining  after  each 
fall  is  not  drawn  back  in  the  burette,  but  is  again  increased 
to  the  falling  point,  and  simply  one  final  reading  made) 
gives  a  mean  value  for  one  drop  that  is  exactly  concordant 
with  that  obtained  from  the  measurement  of  a  single  drop. 
Naturally,  here,  the  greatest  speed  of  formation  of  the  drop 
is  somewhat  over  a  minute,  owing  to  the  small  diameter  of 
the  burette. 

RESUI/TS. 

My  results,  in  detail,  for  the  same  liquids  used  by  Morgan 
and  Stevenson,  and  also  for  carbon  tetrachloride,  are  given 
in  Tables  I  to  VI.  All  my  densities  were  carefully  redeter- 
mined  with  a  25  cubic  centimeters  Ostwald  pykno meter, 
and  agreed  in  the  main  with  those  collected  from  various 
sources  by  R6nard  and  Guye.  With  quinoline,  only,  was  the 
variation  worth  considering,  and  even  that  did  not  change 


II 


appreciably  the  values  of  the  surface  tension  as  given  by 
Re*nard  and  Guye.  The  chemicals  used  were  the  purest 
obtainable.  The  aniline,  pyridine,  benzene  and  chlor- 
benzene  were  Kahlbaum's  "Special  K,"  the  carbon  tetra- 
chloride,  Baker's  "Analyzed"  and  the  quinoline  Merck's 
"Pure  synthetical;"  and  all  showed  the  correct  and  constant 
boiling-points. 

In  the  first  column  of  Tables  I-VI  is  given  the  temperature ; 
the  second  contains  the  actually  determined  drop  volumes, 
all  from  the  same  beveled  tip,  approximately  6  millimeters 
in  diameter ;  the  third  the  average  drop  volume  and  its  mean 
error,  assuming  no  constant  error  to  exist;  the  fourth  the 
density;  the  fifth  the  drop  weight,  the  product  of  the  average 
drop  volume  and  the  density;  the  sixth  the  value 

.  (?)  -.Gf)',  •,•;":- 


/TV          AT* 
12  —  AI 

fwl  and  w2  being  drop  weights  in  milligrams  at  the  tempera- 
tures ^  and  t2,  and  dv  and  d2  the  densities,  while  M  is  the 
molecular  weight.  And,  finally,  the  seventh  column  in 
three  of  the  tables  contains  the  value 

/M 


/My      /M 

\dj  -y2\d2) 


as  calculated  from  Re"nard  and  Guye's  surface  tensions 
(fi  and  7*2)  from  capillary  rise  in  saturated  air.  These  are 
given  where  four  or  more  temperatures  are  employed  to  show 
the  relative  variation  of  the  values  of  Ktemp  and  of  R&iard 
and  Guye's  k,  as  found  for  the  six  liquids,  together  with  the 
critical  temperatures  as  observed  and  as  calculated  from 
Ktemp.  an<*  k,  by  aid  of  the  formulas 

/My 

w\d)  =K,m/>.(r  —  6) 
and 


/My 

\d)  =kO 


—  6)   , 


12 


where  T  is  the  difference  between  the  critical  temperature 
and  that  of  observation.  Here  I  have  used  for  Ktemp  in 
all  cases  the  actually  obtained  results  most  separated  as  to 
temperature,  and  not  those  from  a  smoothed  curve,  as  is 
done  for  the  k  values,  and  has  been  done  by  all  investigators 
using  the  capillary  rise  method. 

In  Figure  4  the  comparative  accuracy  of  drop  weights  and 
the  surface  tensions  by  capillary  rise  for  the  liquids  which 
were  studied  at  three  or  more  temperatures,  is  also  shown 
graphically,  the  surface  tensions  being  the  very  carefully 
determined  ones  of  Re*nard  and  Guye  against  saturated  air. 
It  must  be  noted  here  that  the  graphs  are  only  to  be  com- 
pared in  relative  straightness  and  NOT  AS  TO  SLOPE,  for  I 
have  as  yet  made  no  attempt  to  express  drop  weights  accu- 
rately in  terms  of  surface  tension. 

It  will  be  noted  that  my  two  intermediate  results  for 
pyridine  lie  somewhat  off  the  curve,  one  on  either  side,  al- 
though the  low  and  the  high  values  lead  to  the  satisfactory 
result  for  KUmp  shown  in  Table  VII.  These  errors  are  prob- 
ably due  to  slight  temperature  errors,  for  pyridine  was  the 
first  liquid  investigated,  and  our  first  method  for  the  agita- 
tion of  the  water  in  the  inner  cylinder  was  found  later  to  be 
insufficient.  This  difficulty  was  avoided  at  both  the  low 
and  the  high  temperatures,  these  determinations  having  been 
made  subsequently. 

TABLE  I. 
BENZENE. 


Drop  volume, 
Temp.  cc. 


Mean  volume, 
cc. 


Density. 


Drop 
weight, 
mmg. 


II-4 


30.2 


0.039680 
0.039692 

0.039674 
0.039686 

0.037252 
0.037285 
0.037274 
0.037269 


0.039683     0.888  35.239 
±0.000.003 
or  0.01% 


&  G. 


2.521  1.717 


0.03727       0.868  32.350 
±0.000.007 
or  0.02%  2.583  2 


230 


CO 

6 
2 
.SP 

1 
.2 

I 

1 


-55 


CO 


ft) 


Temperatures. 


FIG.  4. 


Quinolene 

Aniline 

Pyridene 

Chlorbenzene. 
Benzene... 


Drop  weight. 
..      I 
..      2 

.  3 
..  4 
»  5 


Capillary  rise. 


I. — Continued. 


Drop  volume,      Mean  volume, 
Temp.  cc.  cc. 


68.5 


0.034201 

O.O342IO 

0.034191 

0.034202 

0.032076 

0.032090 

00.032081 

0.032074 


Drop 
weight, 
Density.       mmg. 


0.034201      0.844    26.866 
±0.000.004 

or  0.01% 

0.03208       0.827  26.530 
±  o . ooo . 004 
or  0.01% 


.   £R  &  G- 


2.606  2.380 


Drop  volume, 
Temp.  cc. 

(-0.036656 

8.2)0.036700 

10.036684 


39-2 


0.033738 


0.033729 
0-033746 
0-033746 

50.  8fo.  032647 


0.032588 

63.  9fo.  031350 
0.031300 
0.031391 
.0.031359 
'0.030540 


72.2 


0.030523 
0.030540 
0.030529 


TABLE  II. 

CHLORBENZENE. 

Drop 
Mean  volume,  weight, 

cc.  Density.       mmg.        Ktemp.    >&R  &  G- 

0.03668         I.I2OO      41.082 
±0.000.013 

or  0.04%  2.568  2.332 

0-03374         1.0856    36.628 
±0.000.007 

oro.02%  2.590  2.118 

0.03261       1.0730  34-99° 
±0.000.019 

or  0.06%  2.545  2.045 

0.03135 
±0.000.018  1.0590  33.200 

or  0.06% 

2-577  1.938 

0.030533     1.0498  32.054 
±  o . ooo . 004 
or  0.01% 


Temp.   Drop  volume. 

24. 2 fO.OI96OO 
0.019564 
.0.019577 
54. oro. 017516 

0.017505 
JO.OI75IO 
IO.OI75II 


III. 

CARBON  TETRACHLORIDE. 

Drop 
Mean  volume.      Density,      weight.      Kump. 

0.01958         1.5823    39.976 
±0.000.007 

or  0.04%  2.567 

0.017510     1.5240  26.685 
±0.000.003 
or  0.02% 

TABLE  IV. 

PYRIDBNE. 

Dro 


Drop 
Temp.    Drop  volume.         Mean  volume.     Density,      weight.      Ktemp.     /&R&G. 


10.5 


39-2 


58.8 


74-2 


0.046238 
0.046194 
0.646228 

0.042665 
0.042630 
0.042585 
0.042570 
0.042550 
0.040312 

0.040343 
0.040348 
0.040238 
0.040234 
0.038180 
0.038153 
0.038128 
0.038154 


0.04622       0.99I     45-8°4 
±0.000.014 
or  0.036%  2.580  1.57 

0.04260      0.962     40.98 
±0.000.02 
or  0.05% 

2.440  2.54 


Temp.   Drop  volume. 

10.048720 
0.048688 
0.048662 


0.040295     0.943     38.00 
±0.000.025 
or  o .  06% 

0.038154    0.927     35.37 
±0.000.01 
—or  0.025% 

TABLE  V. 
ANILINE. 

Drop 
Mean  volume.     Density,      weight.      Ktemp. 

0.04869       I.OI38   49.362    2.5685 
±0.000.017 

or  0.03% 


2.770  2.31 


TABLE  V '.—Continued. 


Temp.   Drop  volume. 

0.046154 

51-7 

0.046159 

0.046170 

0.046161 

67.1    f  0.044436 

J0.044432 

[0.044428 

Mean  volume.     Density. 


Drop 
weight. 


k  R&  C. 


0.046161  0.9944  45-903 
±  o . ooo . 004 

or  0.01%  2.5700 

0.044432  0.9810  43.588 
±0.000.002 

or  0.01% 

VI. 


Drop 
weight. 


Temp.   Drop  volume.         Mean  volume      Density. 


30. 


M 


0.047456 
0.047504 


55. of  0.045338 

{  0.045347 
[  0.045405 
65.0  f 0.044474 
0.044478 
;o. 044518 


0.04748      1.0852    51.525 
±0.000.024 
— or  0.05% 

0.045363 
±0.000.021     1.0658   48.344 

or  0.05% 


2.580 


2.570 


0.044490 
±0.000.014 
0.03% 


1.0576  47.053 


Showing  Ktemp  k  and  critical  temperatures.  Drop-weight 
results  are  from  the  directly  observed  values  at  the  extreme 
temperatures,  those  from  capillary  rise  being  from  the 
smoothed  curves. 

TABLE  VII. 

Liquid. 

Benzene  ............. 

Chlorbenzene  ......... 

Carbon  tetrachloride    . 
Pyridine  ............. 

Aniline  ...............    2  .  569 

Quinoline  .............    2.575 


Crit. 

Crit.        Observed 

kump.         temp. 

k  R  &  G.     tcmP*      crit.  temp. 

2.569       288.4 

2.12     287.7     ca  288 

2-569     359-5 

2.10     357.7     ca  360 

2.567       285.2 

2.19     278.0     ca  284 

2-567     347-0 

2.07     346-2     ca  344 

2.569    425-8 

2.01     448.6     ca  426 

2.575    520.4 

2.21       496.2        <520 

2.5694+ 

2.n6±o.O965 

0.013 

or  4.6% 

or  0.05% 
Mean  error  of  a  single  result 

±0.0033  or  0.13% 


i6 


DISCUSSION  OF  RESUI/TS. 

A  glance  at  Tables  I-VI  will  show  that  only  in  one  case 
is  my  error  in  the  estimation  of  the  volume  of  a  single  falling 
drop,  assuming  the  existence  of  no  constant  error,  equal  to 
0.07  per  cent.,  all  others  being  very  much  less.  Drop  weights, 
calculated  from  these  volumes  and  the  carefully  redetermined 
densities,  can  then  of  course,  be  burdened  with  no  greater 
error.  From  the  curves  in  Figure  4,  where  drop  weights  in 
milligrams  and  surface  tensions  from  capillary  rise  in  dynes 
are  plotted  against  temperatures,  it  will  be  seen  that  the 
results  of  drop-weights  are  more  concordant  among  them- 
selves, than  are  the  surface  tension  values,  which  allows  of 
but  one  conclusion — the  drop-weight  method  is  more  accurate 
than  that  based  on  capillary  rise,  even  in  the  hands  of  such 
skilful  investigators  as  R6nard  and  Guye.  If  there  is  then 
any  doubt  as  to  the  drop-weight  method  giving  the  TRUE 
relative  values  of  surface  tension,  rather  than  the  method  of 
capillary  rise,  one  need  simply  turn  to  Table  VII,  in  which 
KUmp  for  the  six  non-associated  liquids  used,  is  shown  to  be 
2.5694  ±  0-05  per  cent.,  the  mean  error  of  a  single  result 
being  0.13  per  cent.,  while  the  variation  in  the  corresponding 
average  k  value  by  capillary  rise  is  4.6  per  cent,  from  R£nard 
and  Guye's  results,  and  much  larger  according  to  those  of 
Ramsay  and  Shields'.  When  it  is  remembered  that  the 
Ramsay  and  Shields  formula  from  which  Ktemp  and  k  are 
derived,  which  may  be  written  in  the  form 


/M\l          /MX* 
\\dj  —  x2\d2J 


=  constant 

12~      Al 

where  x  is  a  term  proportional  to  surface  tension,  was  origi- 
nally designed  for  capillary  rise  results,  it  is  quite  evident 
that  drop  weight  is  not  only  also  proportional  to  TRUE 
surface  tension,  but  gives  better  and  more  consistent  values 
for  it  than  capillary  rise.  The  same  reasoning  holds  also 
with  regard  to  the  critical  temperatures,  and  the  Ramsay 
and  Shields  formula  from  which  they  are  calculated  except 


17 

that  here  the  comparison  cannot  be  made  quite  so  satisfac- 
torily, owing  to  necessary  experimental  uncertainty  in  the 
determination  of  critical  temperatures.  Even  here,  how- 
ever, the  drop- weight  method  shows  to  advantage,  for  the 
critical  temperatures  calculated  by  it  for  aniline  and  quinoline 
agree  well  with  the  experimental  values,  where  those  by  aid 
of  capillary  rise  are  quite  different.  Drop  weights,  then, 
satisfy  the  equations  that  were  designed  especially  for  capil- 
lary rise  results  better  than  these  themselves  do. 

This  form  of  proof  of  the  advantage  in  accuracy  of  the 
drop  method  over  that  depending  upon  capillary  rise  is, 
unfortunately,  the  only  one  possible  at  present,  for  even  a 
smoothed  curve  drawn  from  the  capillary  rise  results  is  still 
too  much  burdened  with  error  to  allow  any  very  accurate, 
direct  comparison  of  the  two  methods. 

Owing  to  the  unsatisfactory  nature  of  the  curve  for  the 
surface  tensions  from  capillary  rise,  I  have  omitted  any 
attempt  to  calculate  the  single  values  of  the  Morgan  and 
Stevenson  term  &F  D  ,  for  the  different  liquids  and  tempera- 
tures, but  have  calculated  for  the  sake  of  comparison,  for  I 
have  made  no  other  use  of  it,  one  single  value  of  it  in  the 
following  way :  Since  KUmp  and  k  are  related  to  each  other 
as  the  drop  weights  are  to  the  surface  tensions,  the  ro.tioKfemp  k 
must  give  the  factor  by  which  drop  weights  in  milligrams 
must  be  divided  to  give  TRUE  surface  tensions  in  dynes  per 
centimeter.  This  factor  is  1.2144  since  Ktemp  is  equal  to 
2.5694  and  practically  invariable,  and  the  mean  supposedly 
correct  value  of  kR  &G  is  2.116. 

With  the  exception  of  aniline  and  quinoline  drop  weights 
interpokted  (or  extrapolated)  from  my  curve  agree  with 
those  found  with  the  same  tip  by  Morgan  and  Stevenson 
within  a  few  tenths  of  one  per  cent.  With  aniline  and 
quinoline  the  difference  is  slightly  larger,  but  all  are  well 
within  the  limits  of  error  mentioned  in  their  paper.  These 
slight  errors,  unavoidable  at  that  time  with  their  densities, 
however,  are  sufficient  to  account  for  the  slightly  larger 
value  of  KUmp  and  its  variation  which  they  observed,  i.  e., 


18 

the  value  2.598  ±  1.56  per  cent,  as  compared  to  2.5694  -±- 
0.05  per  cent.,  and  also  for  the  difference  in  KFD  which  in 
average  they  found  to  be  1.226  as  against  my  value  of  1.2144. 
And  the  same  is  true  for  their  critical  temperatures. 

Certainly  the  most  striking  and  important  fact  brought 
out  by  my  work  is  the  practically  absolute  constancy  for  all 
the  liquids  at  all  the  temperatures  of  the  molecular  tem- 
perature coefficient  of  drop  weight,  Ktfmp  for  it  apparently 
makes  the  drop-weight  method  for  large  temperature  in- 
tervals, where  slight  errors  in  temperatures  have  little  effect, 
the  most  accurate  known  method  for  the  determination  of 
molecular  weight,  with  the  exception  of  that  for  permanent 
gases  which  is  based  upon  the  density.  The  truth  of  this  can 
be  shown  by  assuming  as  correct  either  the  maximum, 
minimum  or  the  average  value  of  Ktemp  in  Table  VII,  and 
calculating  from  it  by  aid  of  the  specific  drop  weights  and 
densities  the  molecular  weight  of  any  of  the  liquids  given , 
the  maximum  error  for  any  of  the  six  liquids  being  less  than 
0.05  per  cent,  when  M  for  the  liquid  giving  the  smallest 
value  of  Ktemp  is  calculated  from  the  largest  value  found  for 
KUmp  and  is  very  much  less  when  the  M  for  any  liquid  is 
calculated  from  the  average  K,^  for  it  can  be  readily  shown 
that  the  percentage  variation  in  M  is  equal  to  3/2  the  per- 
centage variation  in  the  Ktemp  used  for  the  calculation. 

Another  advantage  of  the  constant  value  of  KUmp  is  that 
it  is  not  necessary  for  the  calculation  of  the  critical  tem- 
perature from  drop  weight,  as  Ramsay  and  Shields  found  it 
in  using  the  capillary  rise  values  to  first  find  the  exact  value 
of  the  coefficient  for  the  specific  liquid  in  question,  for  I  can 
simply  use  the  value  of  Ktemp  as  found  for  any  other  non- 
associated  liquid. 

SUMMARY. 

i.  An  apparatus  is  described  by  which,  using  the  same 
tip  employed  by  Morgan  and  Stevenson,  the  error  (assuming 
the  existence  of  no  constant  error)  in  the  estimation  of  the 
volume  (and  consequently  of  the  weight)  of  a  single  falling 


19 

drop  is  reduced  to  a  few  hundredths  of  one  per  cent. 

2.  The  elimination  of  their  known  error    and  a  redeter- 
mination   of   the   densities    confirm  all   the   conclusions   of 
Morgan  and  Stevenson,  as  regards  any  one  beveled  tip,  the 
more  accurate  work  simply  accentuating  them  and  proving 
the  drop-weight  method  to  be  even  better  than  they  claimed. 

3.  Drop  weights  calculated  from  the  experimentally  ob- 
served  volumes  by   the  aid   of   redetermined   densities  for 
benzene,     chlorbenzene,     carbon     tetrachloride,    pyridene, 
aniline  and  quinolene,  at  the  same  or  nearly  the  same  tem- 
peratures at  which  the  surface  tensions  from  capillary  rise 
have  been  measured,  show  that  drop  weights  are  proportional 
to  the  temperature,  and  that  the  singly  determined  values 
lie  upon  a  straight  line,  whereas  the  values  from  capillary 
rise  vary  considerably  and  irregularly,  on  the  one  side  or  the 
other  of  such  a  line.     In  other  words,  drop  weight  leads 
more  accurately  to  the  TRUE  surface  tensions  than  does 
capillary  rise. 

4.  The  molecular  temperature  coefficient  of  drop  weight 
calculated  by  aid  of  the  Ramsay  and  Shields  formula 


/M\l         /M\l 

\dj  —  x2\dj 
1  —  --    —  *—  =  constant, 


where  x  is  a  term  proportional  to  surface  tension,  which  was 
designed  especially  for  results  from  capillary  rise,  is  found  for 
the  drop  weight  to  be  practically  invariable  for  all  the  six 
non-associated  liquids,  while  the  use  of  capillary  rise  leads 
to  a  variation  of  6.4  per  cent,  from  the  average  according 
to  the  results  of  R6nard  and  Guye,  and  to  a  still  larger  one, 
according  to  those  of  Ramsay  and  Shields.  The  consequence 
of  this  is  that  the  drop-weight  method  when  used  for  such  a 
temperature  interval  as  I  have  employed  is  the  most  accurate 
method  for  the  determination  of  molecular  weight  known, 
with  the  exception  of  that  for  permanent  gases  as  based 
upon  the  density.  And  critical  temperatures  can  be  more 


2O 


readily  and  accurately  calculated   from  drop   weight  than 

from  capillary  rise,  as  is  shown  for  aniline  and  quinolene  by 

he  agreement  with  experiment  when  calculated  drop  weight 

and  the  wide  divergence  when  calculated  from  capillary  rise. 


Second  Part. 

On   Some    New  Formulae    Relating 
the  Various  Constants  for  Non- 
Associated  Liquids. 


It  was  shown  by  W.  G.  Kistiakowsky1  that  the  relation 


holds  for  a  large  number  of  substances  where  M  =  molecular 
weight  in  liquid  state,  A  =  capillary  constant  (rise  in  a 
capillary  tube  of  unit  radius),  and  T  =  absolute  boiling- 
point,  the  value  of  Kk  varying  from  1.04  to  1.17. 

It  has  been  shown  that  the  drop  weight  of  non-associated 
bodies  is  proportional  to  the  surface  tension,  hence  by  the 
equations 

y  =  -  grhd  and  w  =  vd. 

It  is  obvious  that  by  substituting  b  for  "A"  in  the 
Kistiakowsky  rektion  I  should  obtain  a  constant  similar 
to  that  obtained  from  the  capillary  constant  provided  the 
volume  be  that  delivered  from  unit  tip.  Since  I  have 
insufficient  data  to  enable  me  to  calculate  the  mag- 
nitude of  v  under  those  conditions,  I  must  employ  the  drop 
volume  obtained  in  the  preceding  work.  This  will  not  affect 
the  constancy  of  the  relation  but  will  simply  lead  to  a  new 
empirical  constant. 

*M 

~T  = 

Solving  for  the  extrapolated  values  for  drop  volume  the 
following  results  are  obtained: 

.  f.  Elektrochem.  (8)  375,  1902  and  (12),  513,  615,  1906. 


22 

TABLE  I. 

Substance.  K. 

Benzene 67 . 4 

Pyridene 67 . 3 

Chlorbenzene 68 . 4 

Aniline 67 . 6 

Quinolene 68.8 

Showing  the  statement  to  be  as  generally  justifiable  for 
drop  volume  as  for  capillary  rise  despite  the  extrapolation 
in  the  first  case  since  drop  volumes  have  not  been  estimated 
up  to  the  boiling-point.  In  any  subsequent  use  of  drop- 
volume  determination  as  a  method  for  obtaining  molecular 
weights,  it  would  be  advantageous  if  such  a  formula  as  the 
above  could  be  shown  to  be  general  at  temperatures  other 
than  the  boiling-point,  since  the  molecular  weight  of  a  non- 
associated  body  could  then  be  calculated  from  a  single 
estimation  at  a  temperature  which  would  introduce  no  extra 
experimental  difficulties.  The  most  probable  direction  for 
the  formula  to  take  is  that  of  "corresponding  states"  shown 
to  be  at  least  approximately  true  by  the  following  results: 

TABLE  II. 

Mean  specific  tempera- 
ture coefficient  of  Mean  molecular 
Substance.                                   drop  volume.  co-efficient. 

Benzene 13315  0.0104 

Pyridene 12669  o.oioo 

Chlorbenzene 09605  0.0108 

Quinolene 08717  0.0103 

Aniline m75  0.0104 

Carbon  tetrachloride . . .     06946  o  .0107 


An  agreement  closer  than  that  of  k  (Ramsay  and  Shields) 
by  the  capillary  rise  method  and  derived  direct  from  ex- 
perimental results  not  from  a  smoothed  curve.  It  thus 
seems  probable  that  the  formula 

Mz/__ 

/p    —  -K-(BT  —  T) 


23 

will  be  found  to  hold  at  all  corresponding  temperatures 
where  M  =  molecular  weight,  v  =  drop  volume,  T  =  ab- 
solute temperature  of  observation.  K(BP_T)  =  constant 
for  the  particular  state,  i.  e.,  for  the  difference  between  the 
temperature  of  estimation  and  the  boiling-point.  Solving 
the  equation  for  the  formerly  obtained  experimental  values 
we  obtain  by  extrapolation  the  numbers  shown  in  Table  III. 

The  agreement  is  very  good,  considering  that  the  values 
are  nearly  all  from  extrapolated  drop  volumes,  some,  as  with 
aniline  and  quinoline  over  more  than  100°  C.  The  devia- 
tions from  the  average  are  apparently  no  function  of  the 
molecular  weight  or  boiling-point,  and  are  consequently 
probably  due  largely  to  errors  of  extrapolation.  The  gen- 
eralization is,  however,  likely  only  to  be  accurate  at  tem- 
peratures not  too  far  removed  from  the  boiling-point  as 
evidenced  by  the  increase  of  percentage  variation  in  the 
values  for  K  as  we  retreat  from  the  boiling-point  and  by  the 
fact  that  if  it  held  rigidly  very  far  above  the  boiling-point 
it  would  force  the  conclusion  that  the  critical  temperature 
of  all  non-associated  bodies  lay  at  the  same  distance  from 
their  boiling-point,  a  conclusion  contrary  to  fact. 

Further  work  may  make  it  possible  to  correct  the  formula 
much  as  Trouton's  law  has  been  modified  by  Nernst,  but  for 
the  present  approximate  accuracy  only  is  attainable.  It 
now  remains  to  show  what  may  be  derived  from  the  formula 
in  its  present  state. 

i.  Use  of  the  formula  to  derive  molecular  weight  from  a 
single  drop-volume  determination. 

The  values  used  for  K  are  those  obtained  by  averaging 
the  numbers  shown  in  Table  III,  eliminating  the  values  for 
quinolene  and  aniline  at  temperatures  less  than  80°  from  the 
boiling-point  so  that  all  experimental  values  for  K  are  ex- 
trapolated over  the  same  range. 

The  drop  volumes  used  are  those  directly  obtained,  no 
attempt  being  made  at  mutual  correction,  so  that  the  values 
are  such  as  would  be  obtained  from  isolated  determinations. 


M  W 

w  »> 
<   S 


IO 


.* 


O   M   to  ON 
oo  M  oo  co 


O    <N     Tj- 
M     IO   CN 


•  \0    rovo  00    Ox 


i~>   ON  Tj-  ON  10 

O    O    ON  O    O 


§00 
O 

vS    <N  00    Tt-  ON  ON 
O    ON  ON  ON  ON 


o     1O  M 

">    iO  (N    ON  CO    „ 

ON  ON  00    ON  ON 


*O  co  O 
o     M    ON  vo    O 
•*    ON  rj-  rhoo 

oo  oo  oo  oo 


o     CO  -^-  O  00    ON 
to   CO  M    O    ex    10 

oo  oo  oo  oo  oo 


co  o 


00    ON  CS 


0-    co  t^  >O  O 

M      (\J      M      M      CO 


VO    l^  »O 

.    co  cs  vo 
0    t^  I 

O  vo  vo  VO 


£ 


VO 


00 
ON 


vo 
ON 
M 
ON 


oo 


ON 
VO 
cs 

oo 


ON 

S 


OD 


VO 


'    N    0> 

.  w  a*    ;  a  a 

S8l.i^-S 


25 

TABLE  IV. 


Calculated  molecular  weight 
Boiling-       Molecular         from  experiments  over 
Substance.  point.  weight.  range  of  10°  to  60°  C. 

Chlorbenzene 132  112.4  m.8  — 112.2 

Pyridene 114 .5  78.0  79.  o  —  80.0 

Aniline 183.5  93.0  100.0  — 101.0 

Benzene .  ...  80.4  79.0  79.0  —  80.0 

This  gives  from  estimations  burdened  with  ordinary  ex- 
perimental error  as  close  agreement  as  necessary  for  practical 
work  in  the  laboratory,  even  assuming  the  average  values 
of  K  used  to  be  accurate,  which  is  scarcely  probable.  The 
formula  has  thus  sufficient  accuracy  in  its  present  form  for 
use  in  the  organic  laboratory. 

Mz; 
T 


If  ~J^T  =  K(BP  — T) 


is  generally  true  in  the  neighborhood  of  the  boiling-point, 
it  follows  that 


and  w  =  ; 


hence,  if  the  molecular  weight  of  a  body  be  known  the  value 
of  the  drop  volume  can  be  calculated  by  use  of  the  various 
values  of  K  and  by  using  the  corresponding  value  for  density 
we  can  write  the  formula  of  Ramsay  and  Shields: 

K(BP-T)T 

M 

and  thus  calculate  the  critical  temperature  as  shown  in 
Table  V. 

TABLE  V. 


/M\* 

d\d)  = 


g 

S    3 

-1* 

•- 

§ 

E 

41 

d 

«    ^ 

I    " 

52A 
?S  « 

sj 

1 

j_ 

a 

I 

be 

:l? 

&15 

c3 

1 

§ 

0 

(3 
1 

laS 

**  S  *^, 

S^ri 

<ag 

*Chloroform  

IIQ   4 

6l.2 

262    4. 

26^  o 

260  + 

Chlorbenzole  

*•  "*•  ,7   '  t 
II2.4 

132.0 

*.\J*.     .    Lj. 
356.5 

'•'-'O    v 

359-1 

^  vy  vy  _^ 

360  ± 

*Bthylidene  chloride  .  . 

98.9 

59-2 

255-7 

256.0 

255  ± 

*Toluene  .  . 

Q2.0 

in  .0 

^20.  I 

120.6 

121  4- 

Pyridene  ...........     79.0     114.5     347-75     348-3     345± 


26 


The  density  data  for  the  3  bodies  marked*  were  obtained 
from  smoothed  curves  from  values  published  in  Beilstein 
and  elsewhere. 

The  agreement  is  good,  especially  that  obtained  by  averag- 
ing the  values  over  a  series  of  K's  indicating  the  error  largely 
to  lie  in  their  insufficient  definition.  It  is  also  interesting 
to  note  that  ethylidine  chloride,  toluene  and  chloroform 
give  correct  results  using  as  KteOT^  the  value  established  as  a 
constant  in  previous  work  with  other  bodies,  viz.,  2.569. 

Expressing  in  formula  form  these  results  become 


(2)     ^  =  K(,,mA,(r-6)  =(«OI(K(BP_T)T)I; 


M 

Where  v  =  drop  volume  )  ^  /  t,    1  *  \ 

[  at  temperature  T  (absolute) 
d  =  density  j 

M  =  molecular  weight  T  =  critical  temperature  —  T 
K(B  p  __T)  constant  for  condition  at  boiling-point  —  T  de- 
grees below  boiling-point. 

Since  it  has  been  shown  that  the  critical  temperature  of  a 
body  can  be  calculated  from  a  knowledge  of  its  boiling-point, 
molecular  weight,  and  a  single  density  with  an  accuracy 
equal  to  that  obtainable  by  direct  experimental  determina- 
tion, it  follows  that  we  might  by  substitution  of  such  a  derived 
critical  constant  in  the  Nernst2  modification  of  Van  der 
Waals'  equation,  i,  using  the  boiling-point  as  the  specific 
state,  solve  for  the  critical  pressure:3 


/>,  thus  becoming  unity  and  T  the  boiling-point  of  the  sub 


27 

stance,  Tc  being  the  critical  temperature,  solved  by  equation 

3- 

if  being  thus  obtained,  substitution  of  any  other  value  for  T 
in  Nernst's  equation  leads  to  the  evaluation  of  p  (the  vapor 
pressure)  at  any  temperature. 

With  TT  (critical  pressure)  and  Tc  thus  obtained  the  values 
of  "a"  and  "6"  in  Van  der  Waals'  gas  equation  are  de- 
ter minable 


a- 


64273s    *• 
'  =  «-*-- 

8     273      7T 

and  still  again  knowing  the  value  of  -*  and  p  we  may  obtain 
the  latent  heat  of  vaporization  from  Nernst's1,2  modification 
of  Trouton's  law. 


jt  T^          nP  j% 

7T 

Summing-up,  therefore,  I  find  that  for  a  number  of  un- 
associated  liquids: 

(a)  From  a  knowledge  of  the  boiling-point  of  the  liquid 
and  its  molecular  weight  and  a  density  we  can  by  use  of 
drop-volume  constants  determine  with  very  fair  approxima- 
tion: 

1.  The  surface  tension  (in  terms  of  drop  weight). 

2.  The  critical  temperature  and  pressure,  and  hence, 

3.  The  vapor  pressure  at  any  temperature. 

4.  The  latent  heat  of  evaporation. 

1  Nachrichten  Kgl.  Ges.  Wiss.  Gottingen,  1906. 

3  J.  A.  C.  S.,  "Bingham,"  June,  1906. 

8  Van  der  Waals'  "Die  continuitat  des  Gasformigen  und  Flussigen 
Zustandes,"  pp.  166-167. 

"1st  der  Radius  der  Attraction  bei  alien  Korperm  gleich  gross,  so 
muss  Capillaritatsconstante  fur  die  verschiedenen  Korper  dem  kritischen 
Druck  proportional  sein." 


28 

5.  The  value  of  "a"  and  "6"  in  the  Van  der  Waals'  equa- 
tion for  the  particular  body. 

(6)  From  a  drop-weight  determination,  by  the  same  con- 
stants and  a  knowledge  of  the  boiling-point  we  can  calculate 
the  molecular  weight  of  a  body  and  hence  all  the  values 
under  (a). 

As  to  how  far  the  equations  in  an  unmodified  form  are 
absolutely  general,  insufficient  data  has  yet  been  accumulated 
to  show,  nor  have  the  values  of  K  been  denned  with  sufficient 
accuracy. 

Further  work  must  be  done  upon  this  subject  and  on 
formulae  and  relations  derivable  from  it,  the  present  being 
more  in  the  nature  of  a  note  than  any  attempt  at  a  full 
treatment. 

With  approximate  accuracy  the  values  for  K  are : 

K(B.P.)  =  660        K(B.P.— 20)  =  766        K(B.P. — 40)  =880 

K(B.p._ 10)    =    713    K(B.p.-3o)    =    824  K(Temp.)        =2.569 

LABORATORY  OF  PHYSICAL  CHEMISTRY, 

COLUMBIA  UNIVERSITY, 

April,  1908. 


BIOGRAPHY. 

Brie  Berkeley  Higgins  was  born  August  12,  1885,  in  Sun- 
derland,  Durham,  England.  He  graduated  from  the  Tech- 
nical Institute,  Manchester,  in  1903,  and  Victoria  University, 
Manchester,  in  1906.  Since  that  time  he  has  been  in  the 
employ  of  Messrs.  Crosfield,  Son  &  Company,  of  Warrington, 
England,  from  whom  he  has  obtained  leave  of  absence  to 
complete  his  graduate  work  for  the  Ph.D.  degree  at  Columbia 
University. 


JUH  If- 


6 


Due  end  of  WINlfR  Quarter    u.p  9    ni     87 
subject  to  reca*  after- 

REC'DLD    FEB2371-1PM57 


LD21 


-100».9,'47(A57028l6)«6 


